Adam优化器与梯度修改结合时存在隐藏失效问题，新方法可稳定持续学习。
Hidden Failure Modes of Gradient Modification under Adam in Continual Learning, and Adaptive Decoupled Moment Routing as a Repair
- 将修改后的梯度仅用于一阶矩，保留二阶矩准确性
- 在16域流任务中性能优于最强基线4.5~4.8单位
- 适用于多种梯度修改方法和7B参数规模模型
许多持续学习方法在上游修改梯度（如投影、惩罚重标定、回放混合），同时将Adam视为中性后端。我们发现这种组合存在隐藏失效模式。在高重叠、非自适应的8域持续语言模型中，所有共享路由投影基线均接近原始遗忘水平（12.5–12.8对比13.2）。0.5%回放缓冲区是最强的共享替代方案，但仍达11.6，而固定强度解耦降至14.1，低于原始水平。只有自适应解耦路由保持稳定在9.4，优于原始水平3.8单位。在16域流任务中，其相对于最强共享路由投影基线的提升扩大至4.5–4.8单位。该失效在干净基准上难以察觉。我们通过Adam的二阶矩路径解释此现象：在测试范围内，投影导致旧方向有效学习率按1/(1−α)膨胀，测量值与理论预测误差小于8%，覆盖八个α值。相同冲突也出现在惩罚方法、回放混合及LoRA下的7B规模模型中。我们的修复方案将修改后的梯度仅路由至一阶矩，同时保持幅度忠实的二阶矩统计，并采用重叠感知的自适应强度。这一简单改动是唯一在方法、优化器和规模上均能一致避免崩溃的配置。
原文摘要 · Abstract (English)
Many continual-learning methods modify gradients upstream (e.g., projection, penalty rescaling, replay mixing) while treating Adam as a neutral backend. We show this composition has a hidden failure mode. In a high-overlap, non-adaptive 8-domain continual LM, all shared-routing projection baselines collapse close to vanilla forgetting (12.5--12.8 vs. 13.2). A 0.5% replay buffer is the strongest shared alternative but still reaches 11.6, while fixed-strength decoupling falls below vanilla at 14.1. Only adaptive decoupled routing remains stable at 9.4, improving over vanilla by 3.8 units. On a 16-domain stream, its gain over the strongest shared-routing projection baseline grows to 4.5--4.8 units. The failure is largely invisible on clean benchmarks. We explain this effect through Adam's second-moment pathway: in the tested regime, projection induces a 1/(1-alpha) inflation of the old-direction effective learning rate, matching measurements within 8% across eight alpha values. The same conflict appears with penalty methods, replay mixing, and at 7B scale under LoRA. Our fix routes the modified gradient only to the first moment while preserving magnitude-faithful second-moment statistics, with overlap-aware adaptive strength. This simple change is the only tested configuration that consistently avoids collapse across methods, optimizers, and scale.
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